\(L^2\)-index formula for proper cocompact group actions

DOI10.4171/JNCG/160zbMath1338.19008arXiv1106.4542MaRDI QIDQ744413

Hang Wang

Publication date: 25 September 2014

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4542

zbMATH Keywords

heat kernelKK-theory\(L^2\) indexG-trace

Mathematics Subject Classification ID

Exotic index theories on manifolds (58J22) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Index theory (19K56)

Related Items (12)

Higher genera for proper actions of Lie groups. II: The case of manifolds with boundary ⋮ An index theorem for higher orbital integrals ⋮ An equivariant index for proper actions. I ⋮ Positive scalar curvature and Poincaré duality for proper actions ⋮ An equivariant orbifold index for proper actions ⋮ Heat kernel estimates for the \({{\bar{\partial}}}\)-Neumann problem on \(G\)-manifolds ⋮ Positive scalar curvature and an equivariant Callias-type index theorem for proper actions ⋮ Higher genera for proper actions of Lie groups ⋮ Spin-structures and proper group actions ⋮ Witten genus and elliptic genera for proper actions ⋮ Orbital integrals and \(K\)-theory classes ⋮ Higher localised \(\hat{A}\)-genera for proper actions and applications

Cites Work

• The \(L^2\)-index theorem for homogeneous spaces of Lie groups
• A short proof of the local Atiyah-Singer index theorem
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• Fredholm theories in von Neumann algebras. I
• The index of elliptic operators. III
• On the heat equation and the index theorem
• Curvature and the eigenvalues of the Laplacian for elliptic complexes
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• K-Theoretical Index Theorems for Good Orbifolds
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